# Independent Samples T-Test - Pooled Variance

Where $\bar{x}_i$ is the mean of variable $x$ for the $i$th of $g$ groups, $s_{x_i}$ is its Standard Deviation and $n_i$ its sample size, the test statistic is for the difference between groups $i$ and $i'$ is given by:

$t=\frac{\bar{x}_i-\bar{x}_{i'}}{\sqrt{s^2_x(n^{-1}_i + n^{-1}_{i'})}}$,

where:

$p = 2\Pr(t_v \ge |t|)$,
$v = \sum^g_{i=1} n_i - g$, and
$s^2_{x} = \sum^g_{i=1}{ ( n_i - 1 ) s^2_{x_i}} / v$.